R Under development (unstable) (2024-11-03 r87286 ucrt) -- "Unsuffered Consequences"
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> require(salad)
Loading required package: salad

Attaching package: 'salad'

The following object is masked from 'package:stats':

    dnorm

> set.seed(1)
> x <- dual(sample(1:6))
> A <- x[1:3]
> B <- x[4:6]
> S <- A + B
> P <- A * B
> D <- A - B
> Q <- A / B
> N <- -A
> 
> X <- c(S,P,D,Q,N)
> X0 <- new("dual", x = c(7, 6, 8, 6, 8, 15, -5, 2, -2, 1/6, 
+ 2, 3/5, -1, -4, -3), d = structure(list(x1 = c(1, 0, 0, 6, 0, 
+ 0, 1, 0, 0, 1/6, 0, 0, -1, 0, 0), x2 = c(0, 1, 
+ 0, 0, 2, 0, 0, 1, 0, 0, 0.5, 0, 0, -1, 0), x3 = c(0, 0, 1, 0, 
+ 0, 5, 0, 0, 1, 0, 0, 0.2, 0, 0, -1), x4 = c(1, 0, 0, 1, 0, 0, 
+ -1, 0, 0, -1/36, 0, 0, 0, 0, 0), x5 = c(0, 1, 0, 
+ 0, 4, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0), x6 = c(0, 0, 1, 0, 0, 
+ 3, 0, 0, -1, 0, 0, -0.12, 0, 0, 0)), class = "differential"))
> 
> stopifnot(salad:::test_near_equality(X, X0))
> 
> Z <- (2 + B) + (A - 1) + (1 - B*4) / 3 + 5 / (2*A + 3)
> Z0 <- new("dual", x = c(1.33333333333333, 5.12121212121212, 3.22222222222222
+ ), d = structure(list(x1 = c(0.6, 0, 0), x2 = c(0, 0.917355371900826, 
+ 0), x3 = c(0, 0, 0.876543209876543), x4 = c(-0.333333333333333, 
+ 0, 0), x5 = c(0, -0.333333333333333, 0), x6 = c(0, 0, -0.333333333333333
+ )), class = "differential"))
> 
> stopifnot(salad:::test_near_equality(Z, Z0))
> 
> X2 <- x**2
> A.B <- A**B
> pA <- 3**A
> T <- c(X2, A.B, pA)
> T0 <- new("dual", x = c(1, 16, 9, 36, 4, 25, 1, 16, 243, 3, 81, 27), 
+     d = structure(list(x1 = c(2, 0, 0, 0, 0, 0, 6, 0, 0, 3.29583686600433, 
+     0, 0), x2 = c(0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 88.9875953821169, 
+     0), x3 = c(0, 0, 6, 0, 0, 0, 0, 0, 405, 0, 0, 29.662531794039
+     ), x4 = c(0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0), x5 = c(0, 
+     0, 0, 0, 4, 0, 0, 22.1807097779182, 0, 0, 0, 0), x6 = c(0, 
+     0, 0, 0, 0, 10, 0, 0, 266.962786146351, 0, 0, 0)), class = "differential"))
> 
> stopifnot(salad:::test_near_equality(T, T0))
> 
> 
> # mb <- microbenchmark::microbenchmark(A + B, A * B, A - B, A / B, -A, times = 1000)
> # print(mb)
> 
> # mb <- microbenchmark::microbenchmark(x**2, A**B, 3**A, times = 1000)
> # print(mb)
> 
> # mb <- microbenchmark::microbenchmark((2 + B) + (A - 1) + (1 - B*4) / 3 + 5 / (2*A + 3), times = 1000)
> # print(mb)
> 
> 
> proc.time()
   user  system elapsed 
   0.21    0.06    0.26